That drum roll intro of Buddy Holly’s Peggy Sue
“One two three O’clock four O’clock Rock”
Chuck Berry’s guitar riff opening Johnny B. Goode
Well, somebody had to do it for the Fifties! 
Ok, Elfkin, I’ll play your little game. I see your Under the Bridge and raise you Give it Away, No Rain by Blind Melon, and Natural One by Folk Implosion.
(Sets poker face) 
Ok, first off, I have to second the votes for “Should I Stay or Should I Go” by the Clash and “Blister In The Sun” by Violent Femmes.
But I don’t think you can name “Blister” without “Add It Up”.
“Daaaaaaaaaaaaay After Daaaaaaaaaay…”
Next, I’m proud to be the first to name “Eruption”, by Van Halen (that one trumps “1984” - the keyboard intro to “Jump” - if you ask me)
“I Love Rock And Roll” by Joan Jett & The Blackhearts,
and “Blitzkrieg Bop” & “I Wanna Be Sedated,” both by the Ramones.
opening Bass guitar lead line from “I Saw Your Mommy…” by Suicidal Tendencies
the keyboard and kick drum intro and the guitar line to “Juke Joint Jezebel” by KMFDM
Those are the things that really grab me.
Well, one that comes immediately to mind is the famous bass line from Queen / David Bowe’s “Under Pressure” (I believe Vanilla Ice still claims that he didn’t steal it).
I see a number of 80’s songs listed here. Because of the distinct synthesised sound of many 80’s bands, I imagine a lot of them are immediately recognized because that unmistakable sound - such as “She Blinded me With Science”, “Safety Dance”, “Jump” (as were already mentioned), A-ha’s “Take On Me”, Peter Schilling’s “Major Tom” Or even “Ghostbusters” by Ray Park Jr.
As long as I’m in the 80’s I’ll toss in two more songs with very distinctive openings that would be immediately be recognized by anyone of my generation: Phil Collins’ “In the Air Tonight” and Dexy’s Midnight Runners’ "Come on Eileen.
Can anyone tell when I was in high school?
Hang on, now. I thought we were talking about the riffs that everybody recognizes, not necessarily the ones we like the best.
If it were the latter, I would’ve said the opening to “Unchained” instead of “Jump,” because “Unchained” does rock mightily, and it’s rockin’ Van Halen at its most rockinest (even more rockin than “Eruption,” though that too does rock). But I’ll never forget the day I was listening to Fair Warning in my office and one of my coworkers, a lad not 5 years my junior, said, “Hey, this is pretty cool. What is it?” What is it?!? I went home soon after that and spent the night plucking gray hairs out of my beard.
And I would’ve mentioned “Back in Black,” but it’s a little bit older than me, so it’s not of my generation. Same for the opening riffs of “Misty Mountain Hop,” “Houses of the Holy,” and “Kashmir.”
And I don’t know what all this Dinosaur Jr. and Blur and Quicksand stuff is doing on the list.
Still on recognisable riffs (from my musical era):
The Charlatans : The Only One I Know
Blur : There’s No Other Way
Happy Mondays : Step On
Well of course, that’s why I didn’t say Photograph by The Verve Pipe and Demons by Guster. However, I don’t know many people my age who couldn’t ID the Blur song that was mentioned.
Who’s “everyone”?
“Everyone” I know would recognise Blur. I understand that it isn’t “what’s your favourite riff?” but different people in different countries and in different age groups have different tastes.
If we’re talking about genuine, no-arguments, everyone-with-a-radio-would-know riffs then there aren’t really that many in this thread.
Chumbawamba - Tubthumping.
There was this great commercial a while back … no idea what the product was … which began with a medical staff huddled around an operating table. There’s a “ping” machine nearby that makes two little synthesized beeps every five seconds or so. After a few of these, one of the surgeons starts singing the first lines of “Tainted Love” and is joined, one by one, by everyone else in the room. Soon, they’re all dancing around and I’m thinking: Man, my parents would SO not get that. I’d hazard a guess, however, that most people who went to high school when I did (mid-80’s) would have thought it was kinda groovy.
So, if you consder two notes a riff … that’s my generation-specific contribution.
For something that spans a couple of generations, how about the bass line from Pink Floyd’s “Money”?
Scene: My college dorm room, 1989. Someone in another room is listening to what seems to be a live album.
Roommate: I wonder what that is?
Me: The Doors?
Roommate: No, it doesn’t sound like the Doors.
[dededededededede… Organ riff from Light My Fire kicks in]
Roommate: [clears throat]
Though I loathe the band, Blink 182’s Damnit riff is distinctive and easy to remember.
Tool hit on two awesome riffs with their Aenema album: the main riff from 46+2, plus the opening riff to the title track.
Pearl Jam’s Jeremy and Nirvana’s Smells Like Teen Spirit have great riffs.
Has anybody mentioned:
Land Down Under - Men at Work
Don’t Fear the Reaper - Blue Oyster Cult
Reptile - The Church (unforgetably creepy, which is a good thing cause you never hear the song these days)
Hungry Like the Wolf - Duran Duran
Sweet Caroline - Guns and Roses
So much by U2, especially (IMHO) the intro to “Where the Streets Have No Name”
Most of Dave’s guitar work from Pink Floyd is highly recognizable by many generations, but I can’t speak for anybody more than 5 years younger than me (I’m 29). Ditto Zeppelin… I hope my grandkids will know some of those riffs, but I’m not holding my breath.
Engywook: Once, long ago, might have been on the pushpin board, someone posted about being stuck in traffic when “Who Can It Be Now” came on the radio. He hit his steering wheel in time with the four drumbeats, and looked out his window to see another driver doing the same thing.
I’ve noticed the same phenomenon with the intro to “American Woman” and the “One two three four!” after the instrumental bridge of “Born to Run”.
Sweet Caroline . . . 
If I had to nail some down I’d say
The opening to Pride by U2. I once saw this described as the Edge recreating the universe.
Smells Like Teen Spirit.
Maybe the opening to Machine Head by Bush.
Any Canadian should be able to recognize the riff at the beginning of The Tragically Hip’s “New Orleans is Sinking.”
I’d also suggest the opening chords to Counting Crows’ “Mr. Jones.”
The violin from the verve’s “bittersweet symphony”
The chorus to radiohead’s “creep”
A closet Neil Diamond fan, perhaps…
“I feel fine, dum, dum, dum…good times never felt so good…”
To add to the OP:
Wonderwall, Oasis
Mr Jones, Counting Crows
Layla, Eric Clapton
Summer of 69, Bryan Adams
Brown Sugar, Rolling Stones
Gotta second Sweet Child o’Mine
Other nominations:
Come As You Are - Nirvana
Enter Sandman - Metallica
Today - Smashing Pumpkins
Should I Stay or Should I Go? - The Clash